Merkwaardige producten (MP)

Hoofdmenu Eentje per keer  🖨

Bereken de volgende merkwaardige producten

1. \((-10x^5+4)(-10x^5+4)\)
2. \((s+5)(s-5)\)
3. \((a+1)(a-1)\)
4. \((13y^3+8x)^2\)
5. \((-4q^2-3)(-4q^2+3)\)
6. \((p+12)^2\)
7. \((-2s^4+4q)(-2s^4+4q)\)
8. \((y+6)(y-6)\)
9. \((9s^2+8y)^2\)
10. \((-15y^5-3)^2\)
11. \((y-7)^2\)
12. \((4q^4+13p)(4q^4+13p)\)

---

Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-10x^5+4)(-10x^5+4)=(-10x^5+4)^2=(-10x^5)^2\color{magenta}{+2.(-10x^5).4}+4^2=100x^{10}\color{magenta}{-80x^5}+16\)
2. \((\color{blue}{s}\color{red}{+5})(\color{blue}{s}\color{red}{-5})=\color{blue}{s}^2-\color{red}{5}^2=s^2-25\)
3. \((\color{blue}{a}\color{red}{+1})(\color{blue}{a}\color{red}{-1})=\color{blue}{a}^2-\color{red}{1}^2=a^2-1\)
4. \((13y^3+8x)^2=(13y^3)^2\color{magenta}{+2.(13y^3).(8x)}+(8x)^2=169y^{6}\color{magenta}{+208xy^3}+64x^2\)
5. \((\color{blue}{-4q^2}\color{red}{-3})(\color{blue}{-4q^2}\color{red}{+3})=\color{blue}{(-4q^2)}^2-\color{red}{(-3)}^2=16q^{4}-9\)
6. \((p+12)^2=p^2+\color{magenta}{2.p.12}+12^2=p^2\color{magenta}{+24p}+144\)
7. \((-2s^4+4q)(-2s^4+4q)=(-2s^4+4q)^2=(-2s^4)^2\color{magenta}{+2.(-2s^4).(4q)}+(4q)^2=4s^{8}\color{magenta}{-16qs^4}+16q^2\)
8. \((\color{blue}{y}\color{red}{+6})(\color{blue}{y}\color{red}{-6})=\color{blue}{y}^2-\color{red}{6}^2=y^2-36\)
9. \((9s^2+8y)^2=(9s^2)^2\color{magenta}{+2.(9s^2).(8y)}+(8y)^2=81s^{4}\color{magenta}{+144s^2y}+64y^2\)
10. \((-15y^5-3)^2=(-15y^5)^2\color{magenta}{+2.(-15y^5).(-3)}+(-3)^2=225y^{10}\color{magenta}{+90y^5}+9\)
11. \((y-7)^2=y^2+\color{magenta}{2.y.(-7)}+(-7)^2=y^2\color{magenta}{-14y}+49\)
12. \((4q^4+13p)(4q^4+13p)=(4q^4+13p)^2=(4q^4)^2\color{magenta}{+2.(4q^4).(13p)}+(13p)^2=16q^{8}\color{magenta}{+104pq^4}+169p^2\)